Piping - Flexibility

The industrial revolution has accelerated sharply since the last war, and has been accompanied by the growth of resources which, in turn, have influenced calculation methods.

The advent of the computer has revolutionized these techniques, while at the same time facilitating the worldwide transmission of know-how.

Before the advent of computers, piping studies were limited to very simple cases. A small number of manufacturers have taken advantage of scale model studies, which give very good results, but are relatively costly and time-consuming.

What's more, the examination of these guidelines was mostly limited to calculating the effects of thermal expansion on stresses and strains in the tubes. Other stresses such as weight or wind were taken into account by means of practical rules and approximate calculations.

With the computer, the list of stresses can be extended, and we can tackle iterative calculations, otherwise unthinkable, to solve friction and vibration problems.

As the size of computer memory is virtually limitless, it lends itself to calculations using matrix sets, which make it much easier to formulate, and hence solve, piping problems.

Today, set calculations, and more specifically matrix calculations, are widely taught in schools and universities. It is therefore unnecessary to summarize them in this article, especially as they are used here in a rather elementary form.

The elastic response of piping components to various stresses is mainly in the form of bending, hence the title of this article: Flexibility.

This title covers all piping design methods, and should not be confused with the special "flexibility" method, based on the ability of the various members to deform under the effect of unit loads.

For general structural design equations, please refer to the specialized section in the Basic Sciences treatise.